The science of soulmates: Is there someone out there exactly right for you? On Valentine's Day, there's the temptation to believe that somewhere out there is The One: a soulmate, a perfect match, the person you were meant to be with. Across history, humans have always been drawn to the idea that love isn't random. In ancient Greece, Plato imagined that we were once whole beings with four arms, four legs and two faces, so radiant that Zeus split us in two; ever since, each half has roamed the earth searching for its missing other, a myth that gives the modern soulmate its poetic pedigree and the promise that somewhere, someone will finally make us feel complete. In the Middle Ages, troubadours and Arthurian tales recast that longing as courtly love, a fierce, often forbidden devotion like Lancelot's for Guinevere, in which a knight proved his worth through self-sacrifice for a beloved he might never openly declare.

Curve-straight probabilistic engagement zones (CSPEZ) quantify the spatial regions an evader should avoid to reduce capture risk from a turn-rate-limited pursuer following a curve-straight path with uncertain parameters including position, heading, velocity, range, and maximum turn rate. This paper presents methods for generating evader trajectories that minimize capture risk under such uncertainty. We first derive an analytic solution for the deterministic curve-straight basic engagement zone (CSBEZ), then extend this formulation to a probabilistic framework using four uncertainty-propagation approaches: Monte Carlo sampling, linearization, quadratic approximation, and neural-network regression. We evaluate the accuracy and computational cost of each approximation method and demonstrate how CSPEZ constraints can be integrated into a trajectory-optimization algorithm to produce safe paths that explicitly account for pursuer uncertainty.

Generative models for materials, especially inorganic crystals, hold potential to transform the theoretical prediction of novel compounds and structures. Advancement in this field depends on robust benchmarks and minimal, information-rich datasets that enable meaningful model evaluation. This paper critically examines common datasets and reported metrics for a crystal structure prediction task$\unicode{x2014}$generating the most likely structures given the chemical composition of a material. We focus on three key issues: First, materials datasets should contain unique crystal structures; for example, we show that the widely-utilized carbon-24 dataset only contains $\approx$40% unique structures. Second, materials datasets should not be split randomly if polymorphs of many different compositions are numerous, which we find to be the case for the perov-5 and MP-20 datasets. Third, benchmarks can mislead if used uncritically, e.g., reporting a match rate metric without considering the structural variety exhibited by identical building blocks. To address these oft-overlooked issues, we introduce several fixes. We provide revised versions of the carbon-24 dataset: one with duplicates removed, one deduplicated and split by number of atoms $N$, one with enantiomorphs, and two containing only identical structures but with different unit cells. We also propose new splits for datasets with polymorphs, ensuring that polymorphs are grouped within each split subset, setting a more sensible standard for benchmarking model performance. Finally, we present METRe and cRMSE, new model evaluation metrics that can correct existing issues with the match rate metric.

In this paper, we present a novel theoretical framework for online adaptation of Control Barrier Function (CBF) parameters, i.e., of the class K functions included in the CBF condition, under input constraints. We introduce the concept of locally validated CBF parameters, which are adapted online to guarantee finite-horizon safety, based on conditions derived from Nagumo's theorem and tangent cone analysis. To identify these parameters online, we integrate a learning-based approach with an uncertainty-aware verification process that account for both epistemic and aleatoric uncertainties inherent in neural network predictions. Our method is demonstrated on a VTOL quadplane model during challenging transition and landing maneuvers, showcasing enhanced performance while maintaining safety.

Abstract--Recent work has demonstrated the utility of Random Forest (RF) proximities for various supervised machine learning tasks, including outlier detection, missing data imputation, and visualization. However, the utility of the RF proximities depends upon the success of the RF model, which itself is not the ideal model in all contexts. RF proximities have recently been extended to time series by means of the distance-based Proximity Forest (PF) model, among others, affording time series analysis with the benefits of RF proximities. In this work, we introduce the generalized PF model, thereby extending RF proximities to all contexts in which supervised distance-based machine learning can occur . Additionally, we introduce a variant of the PF model for regression tasks. We also introduce the notion of using the generalized PF model as a meta-learning framework, extending supervised imputation capability to any pre-trained classifier . We experimentally demonstrate the unique advantages of the generalized PF model compared with both the RF model and the k-nearest neighbors model.

We propose a self-supervised machine learning (SSML) framework for multi-fidelity learning and extended predictive soil spectroscopy based on latent space embeddings. A self-supervised representation was pretrained with the large MIR spectral library and the Variational Autoencoder algorithm to obtain a compressed latent space for generating spectral embeddings. At this stage, only unlabeled spectral data were used, allowing us to leverage the full spectral database and the availability of scan repeats for augmented training. We also leveraged and froze the trained MIR decoder for a spectrum conversion task by plugging it into a NIR encoder to learn the mapping between NIR and MIR spectra in an attempt to leverage the predictive capabilities contained in the large MIR library with a low cost portable NIR scanner. This was achieved by using a smaller subset of the KSSL library with paired NIR and MIR spectra. Downstream machine learning models were then trained to map between original spectra, predicted spectra, and latent space embeddings for nine soil properties. The performance of was evaluated independently of the KSSL training data using a gold-standard test set, along with regression goodness-of-fit metrics. Compared to baseline models, the proposed SSML and its embeddings yielded similar or better accuracy in all soil properties prediction tasks. Predictions derived from the spectrum conversion (NIR to MIR) task did not match the performance of the original MIR spectra but were similar or superior to predictive performance of NIR-only models, suggesting the unified spectral latent space can effectively leverage the larger and more diverse MIR dataset for prediction of soil properties not well represented in current NIR libraries.

We used a single RTX 2080 Ti GPU. While T5-small underperforms its larger version, T5-11B, the latter has 11 billion parameters. Gabon and South Africa, are ranked 119th and 121st, respectively . ANSWER: 119th HUMAN: What is Gabon ' s ranking? ColdGAN: What is Gabon ' s rank on the HDI?

Researchers' ability to automate natural language processing has grown exponentially over the past

For example, training such a system to model block-stacking might naturally generalize to stacking other types of objects because of structure in the real world that has been partially captured by the language describing it.

Kolmogorov-Arnold Networks (KANs) are a class of neural networks that have received increased attention in recent literature. In contrast to MLPs, KANs leverage parameterized, trainable activation functions and offer several benefits including improved interpretability and higher accuracy on learning symbolic equations. However, the original KAN architecture requires adjustments to the domain discretization of the network (called the "domain grid") during training, creating extra overhead for the user in the training process. Typical KAN layers are not designed with the ability to autonomously update their domains in a data-driven manner informed by the changing output ranges of previous layers. As an added benefit, this histogram algorithm may also be applied towards detecting out-of-distribution (OOD) inputs in a variety of settings. We demonstrate that AdaptKAN exceeds or matches the performance of prior KAN architectures and MLPs on four different tasks: learning scientific equations from the Feynman dataset, image classification from frozen features, learning a control Lyapunov function, and detecting OOD inputs on the OpenOOD v1.5 benchmark.